Question

Two pyramids are similar. The volume of the larger pyramid is 125 m³ and the volume of the smaller pyramid is 27 m³. The height of the smaller pyramid is 3 m.

What is the height of the larger pyramid?

Answer 1

The height of the larger pyramid is
`5\ m`

Explanation:

Step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

`z^(3)=(125)/(27)\\ \\z=\sqrt[3]{(125)/(27)}\\ \\z=(5)/(3)`

Step 2

Find the height of the larger pyramid

we know that

To find the height of the larger pyramid multiply the scale factor by the height of the smaller pyramid

so

`(5)/(3)(3)=5\ m`

Answer 2

The volume is proportional to the cube of the height. Thus:

3³ : 27
h³ : 125

h = 5 m